3_regularization.ipynb

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   "source": [
    "Deep Learning\n",
    "=============\n",
    "\n",
    "Assignment 3\n",
    "------------\n",
    "\n",
    "Previously in `2_fullyconnected.ipynb`, you trained a logistic regression and a neural network model.\n",
    "\n",
    "The goal of this assignment is to explore regularization techniques."
   ]
  },
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   "source": [
    "# These are all the modules we'll be using later. Make sure you can import them\n",
    "# before proceeding further.\n",
    "from __future__ import print_function\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "from six.moves import cPickle as pickle\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1HrCK6e17WzV"
   },
   "source": [
    "First reload the data we generated in _notmist.ipynb_."
   ]
  },
  {
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     "text": [
      "Training set (200000, 28, 28) (200000,)\n",
      "Validation set (10000, 28, 28) (10000,)\n",
      "Test set (10000, 28, 28) (10000,)\n"
     ]
    }
   ],
   "source": [
    "pickle_file = 'notMNIST.pickle'\n",
    "\n",
    "with open(pickle_file, 'rb') as f:\n",
    "  save = pickle.load(f)\n",
    "  train_dataset = save['train_dataset']\n",
    "  train_labels = save['train_labels']\n",
    "  valid_dataset = save['valid_dataset']\n",
    "  valid_labels = save['valid_labels']\n",
    "  test_dataset = save['test_dataset']\n",
    "  test_labels = save['test_labels']\n",
    "  del save  # hint to help gc free up memory\n",
    "  print('Training set', train_dataset.shape, train_labels.shape)\n",
    "  print('Validation set', valid_dataset.shape, valid_labels.shape)\n",
    "  print('Test set', test_dataset.shape, test_labels.shape)"
   ]
  },
  {
   "cell_type": "markdown",
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    "id": "L7aHrm6nGDMB"
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   "source": [
    "Reformat into a shape that's more adapted to the models we're going to train:\n",
    "- data as a flat matrix,\n",
    "- labels as float 1-hot encodings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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     "text": [
      "Training set (200000, 784) (200000, 10)\n",
      "Validation set (10000, 784) (10000, 10)\n",
      "Test set (10000, 784) (10000, 10)\n"
     ]
    }
   ],
   "source": [
    "image_size = 28\n",
    "num_labels = 10\n",
    "\n",
    "def reformat(dataset, labels):\n",
    "  dataset = dataset.reshape((-1, image_size * image_size)).astype(np.float32)\n",
    "  # Map 2 to [0.0, 1.0, 0.0 ...], 3 to [0.0, 0.0, 1.0 ...]\n",
    "  labels = (np.arange(num_labels) == labels[:,None]).astype(np.float32)\n",
    "  return dataset, labels\n",
    "train_dataset, train_labels = reformat(train_dataset, train_labels)\n",
    "valid_dataset, valid_labels = reformat(valid_dataset, valid_labels)\n",
    "test_dataset, test_labels = reformat(test_dataset, test_labels)\n",
    "print('Training set', train_dataset.shape, train_labels.shape)\n",
    "print('Validation set', valid_dataset.shape, valid_labels.shape)\n",
    "print('Test set', test_dataset.shape, test_labels.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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    "cellView": "both",
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    "colab_type": "code",
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    "id": "RajPLaL_ZW6w"
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   "outputs": [],
   "source": [
    "def accuracy(predictions, labels):\n",
    "  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))\n",
    "          / predictions.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sgLbUAQ1CW-1"
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   "source": [
    "---\n",
    "Problem 1\n",
    "---------\n",
    "\n",
    "Introduce and tune L2 regularization for both logistic and neural network models. Remember that L2 amounts to adding a penalty on the norm of the weights to the loss. In TensorFlow, you can compute the L2 loss for a tensor `t` using `nn.l2_loss(t)`. The right amount of regularization should improve your validation / test accuracy.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Logistic network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "batch_size = 128\n",
    "regularization_beta = 5e-4\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "    # Input data. For the training data, we use a placeholder that will be fed\n",
    "    # at run time with a training minibatch.\n",
    "    tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "    tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "    tf_valid_dataset = tf.constant(valid_dataset)\n",
    "    tf_test_dataset = tf.constant(test_dataset)\n",
    "\n",
    "    # Variables.\n",
    "    weights = tf.Variable(\n",
    "    tf.truncated_normal([image_size * image_size, num_labels]))\n",
    "    biases = tf.Variable(tf.zeros([num_labels]))\n",
    "\n",
    "    # Training computation.\n",
    "    logits = tf.matmul(tf_train_dataset, weights) + biases\n",
    "    loss = tf.reduce_mean(\n",
    "    tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))\n",
    "\n",
    "    # L2 Regularization\n",
    "    \n",
    "    regularization = (tf.nn.l2_loss(weights) + tf.nn.l2_loss(biases))\n",
    "    \n",
    "    loss = loss + regularization_beta * regularization\n",
    "\n",
    "    # Optimizer.\n",
    "    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)\n",
    "\n",
    "    # Predictions for the training, validation, and test data.\n",
    "    train_prediction = tf.nn.softmax(logits)\n",
    "    valid_prediction = tf.nn.softmax(\n",
    "    tf.matmul(tf_valid_dataset, weights) + biases)\n",
    "    test_prediction = tf.nn.softmax(tf.matmul(tf_test_dataset, weights) + biases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 21.694618\n",
      "Minibatch accuracy: 3.1%\n",
      "Validation accuracy: 10.5%\n",
      "Minibatch loss at step 100: 3.207930\n",
      "Minibatch accuracy: 74.2%\n",
      "Validation accuracy: 70.3%\n",
      "Minibatch loss at step 200: 3.808645\n",
      "Minibatch accuracy: 64.1%\n",
      "Validation accuracy: 73.8%\n",
      "Minibatch loss at step 300: 3.452215\n",
      "Minibatch accuracy: 65.6%\n",
      "Validation accuracy: 74.3%\n",
      "Minibatch loss at step 400: 2.937143\n",
      "Minibatch accuracy: 68.8%\n",
      "Validation accuracy: 74.6%\n",
      "Minibatch loss at step 500: 2.684674\n",
      "Minibatch accuracy: 73.4%\n",
      "Validation accuracy: 76.3%\n",
      "Minibatch loss at step 600: 2.386634\n",
      "Minibatch accuracy: 76.6%\n",
      "Validation accuracy: 76.2%\n",
      "Minibatch loss at step 700: 2.341022\n",
      "Minibatch accuracy: 76.6%\n",
      "Validation accuracy: 76.2%\n",
      "Minibatch loss at step 800: 2.505263\n",
      "Minibatch accuracy: 75.8%\n",
      "Validation accuracy: 76.9%\n",
      "Minibatch loss at step 900: 1.930063\n",
      "Minibatch accuracy: 74.2%\n",
      "Validation accuracy: 77.0%\n",
      "Minibatch loss at step 1000: 1.718544\n",
      "Minibatch accuracy: 76.6%\n",
      "Validation accuracy: 77.5%\n",
      "Test accuracy: 84.3%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 1001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 100 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(\n",
    "        valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Neural network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "batch_size = 128\n",
    "hidden_layer_size = 1024\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "    # Input data. For the training data, we use a placeholder that will be fed\n",
    "    # at run time with a training minibatch.\n",
    "    tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "    tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "    tf_valid_dataset = tf.constant(valid_dataset)\n",
    "    tf_test_dataset = tf.constant(test_dataset)\n",
    "\n",
    "    # Variables.\n",
    "    \n",
    "    # Hidden layer (RELU magic)\n",
    "    \n",
    "    weights_hidden = tf.Variable(\n",
    "        tf.truncated_normal([image_size * image_size, hidden_layer_size]))\n",
    "    biases_hidden = tf.Variable(tf.zeros([hidden_layer_size]))\n",
    "    hidden = tf.nn.relu(tf.matmul(tf_train_dataset, weights_hidden) + biases_hidden)\n",
    "\n",
    "    # Output layer\n",
    "\n",
    "    weights_output = tf.Variable(\n",
    "        tf.truncated_normal([hidden_layer_size, num_labels]))\n",
    "    biases_output = tf.Variable(tf.zeros([num_labels]))\n",
    "    \n",
    "    # Training computation.\n",
    "    \n",
    "    logits = tf.matmul(hidden, weights_output) + biases_output\n",
    "    \n",
    "    loss = tf.reduce_mean(\n",
    "        tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))\n",
    "  \n",
    "    # L2 regularization on hidden and output weights and biases\n",
    "    \n",
    "    regularizers = (tf.nn.l2_loss(weights_hidden) + tf.nn.l2_loss(biases_hidden) + \n",
    "                   tf.nn.l2_loss(weights_output) + tf.nn.l2_loss(biases_output))\n",
    "\n",
    "    loss = loss + 5e-4 * regularizers\n",
    "    \n",
    "    # Optimizer.\n",
    "\n",
    "    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)\n",
    "  \n",
    "    # Predictions for the training, validation, and test data.\n",
    "\n",
    "    # Creation of hidden layer of RELU for the validation and testing process\n",
    "    \n",
    "    \n",
    "    train_prediction = tf.nn.softmax(logits)\n",
    "    \n",
    "    hidden_validation = tf.nn.relu(tf.matmul(tf_valid_dataset, weights_hidden) + biases_hidden)\n",
    "    valid_prediction = tf.nn.softmax(\n",
    "    tf.matmul(hidden_validation, weights_output) + biases_output)\n",
    "    \n",
    "    hidden_prediction = tf.nn.relu(tf.matmul(tf_test_dataset, weights_hidden) + biases_hidden)\n",
    "    test_prediction = tf.nn.softmax(tf.matmul(hidden_prediction, weights_output) + biases_output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 526.872559\n",
      "Minibatch accuracy: 8.6%\n",
      "Validation accuracy: 36.9%\n",
      "Minibatch loss at step 100: 185.815399\n",
      "Minibatch accuracy: 79.7%\n",
      "Validation accuracy: 78.5%\n",
      "Minibatch loss at step 200: 186.003693\n",
      "Minibatch accuracy: 77.3%\n",
      "Validation accuracy: 79.7%\n",
      "Minibatch loss at step 300: 151.638336\n",
      "Minibatch accuracy: 77.3%\n",
      "Validation accuracy: 79.7%\n",
      "Minibatch loss at step 400: 151.820618\n",
      "Minibatch accuracy: 75.8%\n",
      "Validation accuracy: 77.5%\n",
      "Minibatch loss at step 500: 150.219498\n",
      "Minibatch accuracy: 75.0%\n",
      "Validation accuracy: 81.2%\n",
      "Minibatch loss at step 600: 126.801460\n",
      "Minibatch accuracy: 77.3%\n",
      "Validation accuracy: 80.6%\n",
      "Minibatch loss at step 700: 115.753525\n",
      "Minibatch accuracy: 82.8%\n",
      "Validation accuracy: 81.0%\n",
      "Minibatch loss at step 800: 111.094269\n",
      "Minibatch accuracy: 82.8%\n",
      "Validation accuracy: 81.2%\n",
      "Minibatch loss at step 900: 106.186508\n",
      "Minibatch accuracy: 76.6%\n",
      "Validation accuracy: 81.5%\n",
      "Minibatch loss at step 1000: 99.702225\n",
      "Minibatch accuracy: 82.0%\n",
      "Validation accuracy: 80.6%\n",
      "Test accuracy: 87.1%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 1001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 100 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(\n",
    "        valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "na8xX2yHZzNF"
   },
   "source": [
    "---\n",
    "Problem 2\n",
    "---------\n",
    "Let's demonstrate an extreme case of overfitting. Restrict your training data to just a few batches. What happens?\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Logistic network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "batch_size = 15\n",
    "regularization_beta = 5e-4\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "    # Input data. For the training data, we use a placeholder that will be fed\n",
    "    # at run time with a training minibatch.\n",
    "    tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "    tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "    tf_valid_dataset = tf.constant(valid_dataset)\n",
    "    tf_test_dataset = tf.constant(test_dataset)\n",
    "\n",
    "    # Variables.\n",
    "    weights = tf.Variable(\n",
    "    tf.truncated_normal([image_size * image_size, num_labels]))\n",
    "    biases = tf.Variable(tf.zeros([num_labels]))\n",
    "\n",
    "    # Training computation.\n",
    "    logits = tf.matmul(tf_train_dataset, weights) + biases\n",
    "    loss = tf.reduce_mean(\n",
    "    tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))\n",
    "\n",
    "    # L2 Regularization\n",
    "    \n",
    "    regularization = (tf.nn.l2_loss(weights) + tf.nn.l2_loss(biases))\n",
    "    \n",
    "    loss = loss + regularization_beta * regularization\n",
    "\n",
    "    # Optimizer.\n",
    "    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)\n",
    "\n",
    "    # Predictions for the training, validation, and test data.\n",
    "    train_prediction = tf.nn.softmax(logits)\n",
    "    valid_prediction = tf.nn.softmax(\n",
    "    tf.matmul(tf_valid_dataset, weights) + biases)\n",
    "    test_prediction = tf.nn.softmax(tf.matmul(tf_test_dataset, weights) + biases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 15.565292\n",
      "Minibatch accuracy: 13.3%\n",
      "Validation accuracy: 12.9%\n",
      "Minibatch loss at step 100: 3.635387\n",
      "Minibatch accuracy: 66.7%\n",
      "Validation accuracy: 69.8%\n",
      "Minibatch loss at step 200: 6.013108\n",
      "Minibatch accuracy: 66.7%\n",
      "Validation accuracy: 71.5%\n",
      "Minibatch loss at step 300: 3.129877\n",
      "Minibatch accuracy: 86.7%\n",
      "Validation accuracy: 74.6%\n",
      "Minibatch loss at step 400: 2.261322\n",
      "Minibatch accuracy: 73.3%\n",
      "Validation accuracy: 74.8%\n",
      "Minibatch loss at step 500: 4.315398\n",
      "Minibatch accuracy: 66.7%\n",
      "Validation accuracy: 73.7%\n",
      "Minibatch loss at step 600: 3.542695\n",
      "Minibatch accuracy: 53.3%\n",
      "Validation accuracy: 73.0%\n",
      "Minibatch loss at step 700: 5.141974\n",
      "Minibatch accuracy: 53.3%\n",
      "Validation accuracy: 73.2%\n",
      "Minibatch loss at step 800: 4.308099\n",
      "Minibatch accuracy: 80.0%\n",
      "Validation accuracy: 75.5%\n",
      "Minibatch loss at step 900: 4.874641\n",
      "Minibatch accuracy: 46.7%\n",
      "Validation accuracy: 75.7%\n",
      "Minibatch loss at step 1000: 1.076668\n",
      "Minibatch accuracy: 93.3%\n",
      "Validation accuracy: 76.1%\n",
      "Test accuracy: 82.6%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 1001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 100 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(\n",
    "        valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Neural Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "batch_size = 10\n",
    "hidden_layer_size = 1024\n",
    "regularization_beta = 5e-4\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "    # Input data. For the training data, we use a placeholder that will be fed\n",
    "    # at run time with a training minibatch.\n",
    "    tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "    tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "    tf_valid_dataset = tf.constant(valid_dataset)\n",
    "    tf_test_dataset = tf.constant(test_dataset)\n",
    "\n",
    "    # Variables.\n",
    "    \n",
    "    # Hidden layer (RELU magic)\n",
    "    \n",
    "    weights_hidden = tf.Variable(\n",
    "        tf.truncated_normal([image_size * image_size, hidden_layer_size], \n",
    "                           stddev=1 / math.sqrt(float(image_size * image_size))))\n",
    "    biases_hidden = tf.Variable(tf.zeros([hidden_layer_size]))\n",
    "    hidden = tf.nn.relu(tf.matmul(tf_train_dataset, weights_hidden) + biases_hidden)\n",
    "\n",
    "    # Output layer\n",
    "\n",
    "    weights_output = tf.Variable(\n",
    "        tf.truncated_normal([hidden_layer_size, num_labels]))\n",
    "    biases_output = tf.Variable(tf.zeros([num_labels]))\n",
    "    \n",
    "    # Training computation.\n",
    "    \n",
    "    logits = tf.matmul(hidden, weights_output) + biases_output\n",
    "    \n",
    "    loss = tf.reduce_mean(\n",
    "        tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))\n",
    "  \n",
    "    # L2 regularization on hidden and output weights and biases\n",
    "    \n",
    "    regularizers = (tf.nn.l2_loss(weights_hidden) + tf.nn.l2_loss(biases_hidden) + \n",
    "                   tf.nn.l2_loss(weights_output) + tf.nn.l2_loss(biases_output))\n",
    "\n",
    "    loss = loss + regularization_beta * regularizers\n",
    "    \n",
    "    # Optimizer.\n",
    "\n",
    "    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)\n",
    "  \n",
    "    # Predictions for the training, validation, and test data.\n",
    "\n",
    "    # Creation of hidden layer of RELU for the validation and testing process\n",
    "    \n",
    "    \n",
    "    train_prediction = tf.nn.softmax(logits)\n",
    "    \n",
    "    hidden_validation = tf.nn.relu(tf.matmul(tf_valid_dataset, weights_hidden) + biases_hidden)\n",
    "    valid_prediction = tf.nn.softmax(\n",
    "    tf.matmul(hidden_validation, weights_output) + biases_output)\n",
    "    \n",
    "    hidden_prediction = tf.nn.relu(tf.matmul(tf_test_dataset, weights_hidden) + biases_hidden)\n",
    "    test_prediction = tf.nn.softmax(tf.matmul(hidden_prediction, weights_output) + biases_output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 17.594547\n",
      "Minibatch accuracy: 10.0%\n",
      "Validation accuracy: 22.9%\n",
      "Minibatch loss at step 100: 363.727203\n",
      "Minibatch accuracy: 40.0%\n",
      "Validation accuracy: 49.7%\n",
      "Minibatch loss at step 200: 1038.084106\n",
      "Minibatch accuracy: 70.0%\n",
      "Validation accuracy: 50.5%\n",
      "Minibatch loss at step 300: 19686.111328\n",
      "Minibatch accuracy: 60.0%\n",
      "Validation accuracy: 50.1%\n",
      "Minibatch loss at step 400: 59617.957031\n",
      "Minibatch accuracy: 30.0%\n",
      "Validation accuracy: 39.8%\n",
      "Minibatch loss at step 500: 21538.439453\n",
      "Minibatch accuracy: 50.0%\n",
      "Validation accuracy: 48.6%\n",
      "Minibatch loss at step 600: 62233.554688\n",
      "Minibatch accuracy: 60.0%\n",
      "Validation accuracy: 56.5%\n",
      "Minibatch loss at step 700: 62330.300781\n",
      "Minibatch accuracy: 30.0%\n",
      "Validation accuracy: 51.4%\n",
      "Minibatch loss at step 800: 18765.556641\n",
      "Minibatch accuracy: 60.0%\n",
      "Validation accuracy: 54.1%\n",
      "Minibatch loss at step 900: 163009.171875\n",
      "Minibatch accuracy: 40.0%\n",
      "Validation accuracy: 44.2%\n",
      "Minibatch loss at step 1000: 185813.250000\n",
      "Minibatch accuracy: 50.0%\n",
      "Validation accuracy: 47.4%\n",
      "Test accuracy: 51.9%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 1001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 100 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(\n",
    "        valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ww3SCBUdlkRc"
   },
   "source": [
    "---\n",
    "Problem 3\n",
    "---------\n",
    "Introduce Dropout on the hidden layer of the neural network. Remember: Dropout should only be introduced during training, not evaluation, otherwise your evaluation results would be stochastic as well. TensorFlow provides `nn.dropout()` for that, but you have to make sure it's only inserted during training.\n",
    "\n",
    "What happens to our extreme overfitting case?\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "batch_size = 20\n",
    "hidden_layer_size = 2048 # Doubled because half of the results are discarded\n",
    "regularization_beta = 5e-4\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "    # Input data. For the training data, we use a placeholder that will be fed\n",
    "    # at run time with a training minibatch.\n",
    "    tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "    tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "    tf_valid_dataset = tf.constant(valid_dataset)\n",
    "    tf_test_dataset = tf.constant(test_dataset)\n",
    "\n",
    "    # Variables.\n",
    "    \n",
    "    # Hidden layer (RELU magic)\n",
    "    \n",
    "    weights_hidden = tf.Variable(\n",
    "        tf.truncated_normal([image_size * image_size, hidden_layer_size], \n",
    "                           stddev=1 / math.sqrt(float(image_size * image_size))))\n",
    "    biases_hidden = tf.Variable(tf.zeros([hidden_layer_size]))\n",
    "    hidden = tf.nn.relu(tf.matmul(tf_train_dataset, weights_hidden) + biases_hidden)\n",
    "\n",
    "    # Output layer\n",
    "\n",
    "    weights_output = tf.Variable(\n",
    "        tf.truncated_normal([hidden_layer_size, num_labels]))\n",
    "    biases_output = tf.Variable(tf.zeros([num_labels]))\n",
    "    \n",
    "    # Training computation.\n",
    "    \n",
    "    logits = tf.matmul(tf.nn.dropout(hidden, 0.5), weights_output) + biases_output\n",
    "    \n",
    "    loss = tf.reduce_mean(\n",
    "        tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))\n",
    "  \n",
    "    # L2 regularization on hidden and output weights and biases\n",
    "    \n",
    "    regularizers = (tf.nn.l2_loss(weights_hidden) + tf.nn.l2_loss(biases_hidden) + \n",
    "                   tf.nn.l2_loss(weights_output) + tf.nn.l2_loss(biases_output))\n",
    "\n",
    "    loss = loss + regularization_beta * regularizers\n",
    "    \n",
    "    # Optimizer.\n",
    "\n",
    "    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)\n",
    "  \n",
    "    # Predictions for the training, validation, and test data.\n",
    "\n",
    "    # Creation of hidden layer of RELU for the validation and testing process\n",
    "    \n",
    "    \n",
    "    train_prediction = tf.nn.softmax(logits)\n",
    "    \n",
    "    hidden_validation = tf.nn.relu(tf.matmul(tf_valid_dataset, weights_hidden) + biases_hidden)\n",
    "    valid_prediction = tf.nn.softmax(\n",
    "    tf.matmul(hidden_validation, weights_output) + biases_output)\n",
    "    \n",
    "    hidden_prediction = tf.nn.relu(tf.matmul(tf_test_dataset, weights_hidden) + biases_hidden)\n",
    "    test_prediction = tf.nn.softmax(tf.matmul(hidden_prediction, weights_output) + biases_output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 33.598904\n",
      "Minibatch accuracy: 0.0%\n",
      "Validation accuracy: 29.6%\n",
      "Minibatch loss at step 100: 606879.562500\n",
      "Minibatch accuracy: 40.0%\n",
      "Validation accuracy: 45.3%\n",
      "Minibatch loss at step 200: 98750320.000000\n",
      "Minibatch accuracy: 35.0%\n",
      "Validation accuracy: 44.4%\n",
      "Minibatch loss at step 300: 3396855552.000000\n",
      "Minibatch accuracy: 40.0%\n",
      "Validation accuracy: 49.5%\n",
      "Minibatch loss at step 400: 122310983680.000000\n",
      "Minibatch accuracy: 40.0%\n",
      "Validation accuracy: 52.5%\n",
      "Minibatch loss at step 500: 3976950972416.000000\n",
      "Minibatch accuracy: 45.0%\n",
      "Validation accuracy: 46.1%\n",
      "Minibatch loss at step 600: 148167228129280.000000\n",
      "Minibatch accuracy: 30.0%\n",
      "Validation accuracy: 49.6%\n",
      "Minibatch loss at step 700: 23460502940155904.000000\n",
      "Minibatch accuracy: 45.0%\n",
      "Validation accuracy: 45.3%\n",
      "Minibatch loss at step 800: 2254988534844751872.000000\n",
      "Minibatch accuracy: 40.0%\n",
      "Validation accuracy: 40.7%\n",
      "Minibatch loss at step 900: 39728526103081385984.000000\n",
      "Minibatch accuracy: 55.0%\n",
      "Validation accuracy: 47.4%\n",
      "Minibatch loss at step 1000: 2287284660311718625280.000000\n",
      "Minibatch accuracy: 25.0%\n",
      "Validation accuracy: 54.4%\n",
      "Test accuracy: 58.6%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 1001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 100 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(\n",
    "        valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-b1hTz3VWZjw"
   },
   "source": [
    "---\n",
    "Problem 4\n",
    "---------\n",
    "\n",
    "Try to get the best performance you can using a multi-layer model! The best reported test accuracy using a deep network is [97.1%](http://yaroslavvb.blogspot.com/2011/09/notmnist-dataset.html?showComment=1391023266211#c8758720086795711595).\n",
    "\n",
    "One avenue you can explore is to add multiple layers.\n",
    "\n",
    "Another one is to use learning rate decay:\n",
    "\n",
    "    global_step = tf.Variable(0)  # count the number of steps taken.\n",
    "    learning_rate = tf.train.exponential_decay(0.5, step, ...)\n",
    "    optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)\n",
    " \n",
    " ---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "batch_size = 128\n",
    "hidden_layer_size = 2048 # Doubled because half of the results are discarded\n",
    "regularization_beta = 5e-4\n",
    "\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "    # Input data. For the training data, we use a placeholder that will be fed\n",
    "    # at run time with a training minibatch.\n",
    "    tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "    tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "    tf_valid_dataset = tf.constant(valid_dataset)\n",
    "    tf_test_dataset = tf.constant(test_dataset)\n",
    "\n",
    "    # Variables.\n",
    "    \n",
    "    # Hidden layer (RELU magic)\n",
    "    \n",
    "    weights_hidden_1 = tf.Variable(\n",
    "        tf.truncated_normal([image_size * image_size, hidden_layer_size], \n",
    "                           stddev=1 / math.sqrt(float(image_size * image_size))))\n",
    "    biases_hidden_1 = tf.Variable(tf.zeros([hidden_layer_size]))\n",
    "    hidden_1 = tf.nn.relu(tf.matmul(tf_train_dataset, weights_hidden_1) + biases_hidden_1)\n",
    "\n",
    "    weights_hidden_2 = tf.Variable(tf.truncated_normal([hidden_layer_size, hidden_layer_size],\n",
    "                                                      stddev=1 / math.sqrt(float(image_size * image_size))))\n",
    "    biases_hidden_2 = tf.Variable(tf.zeros([hidden_layer_size]))\n",
    "    hidden_2 = tf.nn.relu(tf.matmul(tf.nn.dropout(hidden_1, 0.5), weights_hidden_2) + biases_hidden_2)\n",
    "    \n",
    "    # Output layer\n",
    "\n",
    "    weights_output = tf.Variable(\n",
    "        tf.truncated_normal([hidden_layer_size, num_labels],\n",
    "                           stddev=1 / math.sqrt(float(image_size * image_size))))\n",
    "    biases_output = tf.Variable(tf.zeros([num_labels]))\n",
    "    \n",
    "    # Training computation.\n",
    "    \n",
    "    logits = tf.matmul(tf.nn.dropout(hidden_2, 0.5), weights_output) + biases_output\n",
    "    \n",
    "    loss = tf.reduce_mean(\n",
    "        tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))\n",
    "  \n",
    "    # L2 regularization on hidden and output weights and biases\n",
    "    \n",
    "    regularizers = (tf.nn.l2_loss(weights_hidden_1) + tf.nn.l2_loss(biases_hidden_1) + \n",
    "                    tf.nn.l2_loss(weights_hidden_2) + tf.nn.l2_loss(biases_hidden_2) +\n",
    "                    tf.nn.l2_loss(weights_output) + tf.nn.l2_loss(biases_output))\n",
    "\n",
    "    loss = loss + regularization_beta * regularizers\n",
    "    \n",
    "    # Optimizer.\n",
    "\n",
    "    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)\n",
    "  \n",
    "    # Predictions for the training, validation, and test data.\n",
    "\n",
    "    # Creation of hidden layer of RELU for the validation and testing process\n",
    "    \n",
    "    \n",
    "    train_prediction = tf.nn.softmax(logits)\n",
    "    \n",
    "    hidden_validation_1 = tf.nn.relu(tf.matmul(tf_valid_dataset, weights_hidden_1) + biases_hidden_1)\n",
    "    hidden_validation_2 = tf.nn.relu(tf.matmul(hidden_validation_1, weights_hidden_2) + biases_hidden_2)\n",
    "    valid_prediction = tf.nn.softmax(\n",
    "    tf.matmul(hidden_validation_2, weights_output) + biases_output)\n",
    "    \n",
    "    hidden_prediction_1 = tf.nn.relu(tf.matmul(tf_test_dataset, weights_hidden_1) + biases_hidden_1)\n",
    "    hidden_prediction_2 = tf.nn.relu(tf.matmul(hidden_prediction_1, weights_hidden_2) + biases_hidden_2)\n",
    "    test_prediction = tf.nn.softmax(tf.matmul(hidden_prediction_2, weights_output) + biases_output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 3.991061\n",
      "Minibatch accuracy: 12.5%\n",
      "Validation accuracy: 21.9%\n",
      "Minibatch loss at step 500: 1.806115\n",
      "Minibatch accuracy: 80.5%\n",
      "Validation accuracy: 85.2%\n",
      "Minibatch loss at step 1000: 1.308846\n",
      "Minibatch accuracy: 88.3%\n",
      "Validation accuracy: 86.6%\n",
      "Minibatch loss at step 1500: 1.291549\n",
      "Minibatch accuracy: 82.0%\n",
      "Validation accuracy: 86.9%\n",
      "Minibatch loss at step 2000: 1.065349\n",
      "Minibatch accuracy: 89.1%\n",
      "Validation accuracy: 87.5%\n",
      "Minibatch loss at step 2500: 1.003274\n",
      "Minibatch accuracy: 87.5%\n",
      "Validation accuracy: 88.3%\n",
      "Minibatch loss at step 3000: 0.961374\n",
      "Minibatch accuracy: 81.2%\n",
      "Validation accuracy: 88.1%\n",
      "Minibatch loss at step 3500: 0.813373\n",
      "Minibatch accuracy: 87.5%\n",
      "Validation accuracy: 88.0%\n",
      "Minibatch loss at step 4000: 0.857690\n",
      "Minibatch accuracy: 83.6%\n",
      "Validation accuracy: 88.8%\n",
      "Minibatch loss at step 4500: 0.756531\n",
      "Minibatch accuracy: 85.2%\n",
      "Validation accuracy: 88.5%\n",
      "Minibatch loss at step 5000: 0.602770\n",
      "Minibatch accuracy: 88.3%\n",
      "Validation accuracy: 88.7%\n",
      "Minibatch loss at step 5500: 0.698459\n",
      "Minibatch accuracy: 86.7%\n",
      "Validation accuracy: 89.1%\n",
      "Minibatch loss at step 6000: 0.492098\n",
      "Minibatch accuracy: 92.2%\n",
      "Validation accuracy: 89.1%\n",
      "Minibatch loss at step 6500: 0.529292\n",
      "Minibatch accuracy: 90.6%\n",
      "Validation accuracy: 89.0%\n",
      "Minibatch loss at step 7000: 0.579818\n",
      "Minibatch accuracy: 87.5%\n",
      "Validation accuracy: 88.4%\n",
      "Minibatch loss at step 7500: 0.640730\n",
      "Minibatch accuracy: 85.2%\n",
      "Validation accuracy: 89.0%\n",
      "Minibatch loss at step 8000: 0.509321\n",
      "Minibatch accuracy: 89.1%\n",
      "Validation accuracy: 88.7%\n",
      "Minibatch loss at step 8500: 0.633269\n",
      "Minibatch accuracy: 86.7%\n",
      "Validation accuracy: 89.6%\n",
      "Minibatch loss at step 9000: 0.579485\n",
      "Minibatch accuracy: 85.9%\n",
      "Validation accuracy: 89.1%\n",
      "Minibatch loss at step 9500: 0.489396\n",
      "Minibatch accuracy: 89.1%\n",
      "Validation accuracy: 88.8%\n",
      "Minibatch loss at step 10000: 0.708435\n",
      "Minibatch accuracy: 81.2%\n",
      "Validation accuracy: 89.4%\n",
      "Test accuracy: 94.3%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 10001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 500 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(\n",
    "        valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  }
 ],
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